468 MEASUREMENT OF CAPACITY. DIELECTRICS. 



A mechanical arrangement is necessary to make the oscillations 

 of the rocking commutator regular ; the result is obtained more 

 easily with a rotating commutator. 



1057. In this method it has been supposed that at each ope- 

 ration the contact is long enough for the discharge to be complete. 

 Suppose this is not the case. Let R be the resistance of the circuit 

 comprising the connections with the condenser, and m the charge of 

 the condenser at the time /. If the effects of induction may be neg- 

 lected, the current is defined by the equation 



o 

 . = 0, 



C at 



^ or, if M is the initial charge, before the reversal, 



X 



m = (M + EC)e~ - EC . 



During the time of contact 0, the charge passes from +M to 

 M, which gives 



^ M^ + e-~)=EC^-e- 



7> The mean current I is equal to M or 2^M, according as the 



discharges are simple, or with the reversal of the condenser. In the 

 second case, for instance, we have 



0_ 



I 6 ~ RC 



i+e~^c 



1058. DIRECT COMPARISON OF CAPACITIES WITH RESISTANCES. 

 Let us consider the problem more generally. Between two points N 

 and P of a network of conductors containing constant electromotive 

 forces a capacity C is inserted, and by one of the preceding arrange- 

 ments it is discharged n times per second. If E is the difference of 

 potential of the two points in the permanent regime, and if we 

 suppose that after each break the current has time to re-establish 

 itself, the quantity of electricity which in each second traverses the 

 connecting wire is, with the second method of breaking, 



